{
  "id": "math/0603368",
  "version": "v1",
  "published": "2006-03-15T12:10:23.000Z",
  "updated": "2006-03-15T12:10:23.000Z",
  "title": "Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves",
  "authors": [
    "Ildefonso Castro",
    "Bang-yen Chen"
  ],
  "comment": "16 pages To be published in Tohoku Mathematical Journal",
  "journal": "Tohoku Math. J. 58 (2006), 565-579",
  "categories": [
    "math.DG"
  ],
  "abstract": "We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in complex Euclidean plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-15T12:10:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D12",
      "53C40"
    ],
    "keywords": [
      "complex euclidean plane",
      "lagrangian surfaces",
      "hyperbolic curves",
      "constant mean curvature",
      "willmore surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3368C"
    }
  }
}